The document describes using Generalised Semi-linear Canonical Correlation Analysis (GSLCCA) to analyze EEG data from a drug experiment and identify the effect of different doses of clonidine on brain activity over time. GSLCCA fits a pharmacokinetic model to the EEG power spectra data and extracts "signatures" representing the contribution of different brain frequencies to the drug's time-dependent response. The analysis revealed dose-dependent changes in the signatures compared to vehicle control, indicating clonidine had an active effect on brain activity as expected.

1. Detecting Drug Effects in the Brain
Heather Turner, Phil Brain and Foteini Strimenopoulou
Nonclinical Statistics
Pfizer, UK
18 August 2011

2. Background
Aim: identify and characterise effect of drug on the brain
• Drug effect over time
PK/PD model
• EEG experiments
electrical activity in the brain
• Generalised Semi-linear Canonical Correlation Analysis
(GSLCCA)

3. EEG
• Electrodes placed on scalp
• Monitor difference in voltage between baseline electrode
and others
• Produces virtually continuous signal

4. EEG Data
• EEG signal converted via FFT to power spectra
”amount” of each frequency for each time slice
multivariate response over time
Examples of frequency periodograms
0.00030
q
0−5 minutes
120−125 minutes
0.00020
q q
FFT Power (µV2)
−→
− q
q q
0.00010
qq
q q
qqqq
qq q
q q q
q q
q q
q q q
qqq q
0.00000
qqqqqq
qqqqqqqqqq
qqqqqqqqq
qqqq
0 5 10 15 20 25 30 35
Frequency (Hz)

5. PK/PD
• Assumptions
drug level in brain follows pharmacokinetics model (PK)
brain response proportional to dose level (PD)
• Expected response over time follows PK model, e.g.
Double Exponential
β(exp(−k1 t) − exp(−k2 t))
Critical Exponential
βtexp(−k1 t)

6. PK Models
0.4
Double Exponential
0.3
0.2 Critical Exponential
Response
0.1
0.0
−0.2
0 10000 20000 30000 40000
Time

7. GSLCCA (in pictures)
Spectrum
"Observed" Value
0.00020
Power (µV2)
0.00000
0.2
0 5 15 25 35
Frequency (Hz)
0.1
Response
× −→
0.0
Signature
500 1000
Coefficient
−0.1
0
−500
0 10000 20000 30000 40000
0 5 15 25 35
Time
Frequency (Hz)

8. GSLCCA (in pictures)
Spectrum
Fitted Values
0.00020
Power (µV2)
q
q
q
q q
0.00000
q
0.2
q q
q
q
q
q
0 5 15 25 35 q
q
q
q
Frequency (Hz)
0.1
Response
q q q
× −→ q
q
0.0
q
q
Signature q q q
q
q
500 1000
qq q
qq q q q q
q qq
q q q q qq
q q
q q q q
Coefficient
q q q
−0.1
q q
q qq
q
q q q q
q q
q
qq
q
q
0
−500
0 10000 20000 30000 40000
0 5 15 25 35
Time
Frequency (Hz)

9. GSLCCA Method
• Canonical Correlation Analysis (CCA)
For matrices Y and X, finds loadings a and b to
maximise
cor(Y a, Xb)
• Semi-linear
Y is the matrix of power spectra
X = X(t, θ) defined by PK model
• Generalised
linear coefficients b or nonlinear parameters θ may
depend on treatment factor

10. gslcca Package
• gslcca function
specify PK model by name/formula
specify which parameters vary by treatment
control over data smoothing
partial CCA option
• plot, print, summary

11. Clonidine Experiment
• 4 treatments
Control
Low dose
Medium dose
High dose
• 8 rats in 4-period cross-over design
• EEG data recorded for 12 hours post-dose

12. GSLCCA Analysis
Call:
gslcca(Y = spectra, formula = "Critical Exponential", time = Time,
subject = Rat, treatment = Treatment, separate = TRUE, ref = 1,
data = design, subject.smooth = 4)
GSLCCA based on 8 subjects
Data smoothed at subject level using 4 roots
Nonlinear parameters:
subject 35 subject 36 subject 37 subject 38
K1 Low Dose 7.5576 8.4252 7.8778 9.9125
K1 Middle Dose 7.8786 8.5137 8.0901 8.8885
K1 High Dose 8.9017 9.3213 9.0159 9.1980
subject 39 subject 40 subject 41 subject 42
K1 Low Dose 8.7217 8.0102 8.7103 8.1199
K1 Middle Dose 8.8546 8.5952 9.1854 8.3800
K1 High Dose 9.0439 9.1611 9.3047 8.9933

13. Fitted Model
plot(result, "fitted")

14. Observed + Fitted
plot(result, "scores")

15. Signatures
plot(result, "signatures")
Signatures Corresponding to Different Subjects
Subject 35
Subject 36
Subject 37
500
Subject 38
Subject 39
Subject 40
Subject 41
Subject 42
Coefficient
0
−500
0 5 10 15 20 25 30 35
Frequency (Hz)

16. Normalised Signatures
Signatures Corresponding to Different Subjects
Subject 35
Subject 36
0.6 Subject 37
Subject 38
Subject 39
0.4
Subject 40
Subject 41
Subject 42
0.2
Coefficient
0.0
−0.2
−0.4
0 5 10 15 20 25 30 35
Frequency (Hz)

17. Mean Signature
Mean Signature
0.6
• contribution of power
0.4
at each frequency to
PK curve over time
Coefficient
0.2
• assumed to be specific
0.0
to the target drug is
aimed at
−0.2
0 5 10 15 20 25 30 35
Frequency (Hz)

18. 0.6
0.4 Control/Inactive Signature
• if drug inactive, any
dose ≡ control
Coefficient
0.2
• inactive drug has same
0.0
signature as control
−0.2
0 5 10 15 20 25 30 35
Frequency

19. 0.6 Control/Inactive Signature
clonidine
vehicle
0.4
• In this case drug clearly
different from control
Coefficient
0.2
• Drug is active - as
0.0
expected!
−0.2
0 5 10 15 20 25 30 35
Frequency

20. 200 Comparing Active Drugs
Drug A
Drug B
• Two drugs targeting
150
same ion channel,
100
different receptors
Coefficient
50
• Run t-tests to compare
0
loadings at each
−50
frequency
−100
0 20 40 60 80
Frequency

21. 3.0 Snapshot Analysis
delta
theta
alpha
2.5
beta
gamma • P-values adjusted using
2.0
− log10(p)
FDR
1.5
• Frequencies split into
1.0
conventional bands
0.5
0.0
0 20 40 60 80
Frequency

22. Summary
gslcca package is in development on R-Forge
https://r-forge.r-project.org/projects/gslcca/
Further work needed before release to CRAN, e.g.
• fitting PK/PD model to all rats simultaneously
• adjusting for control response